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author	Sandro Tosi <sandro.tosi@gmail.com>	2011-10-31 16:15:39 (GMT)
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\chapter{Expressions and conditions} \index{expression} \index{condition} {\bf Note:} In this and the following chapters, extended BNF notation will be used to describe syntax, not lexical analysis. \index{BNF} This chapter explains the meaning of the elements of expressions and conditions. Conditions are a superset of expressions, and a condition may be used wherever an expression is required by enclosing it in parentheses. The only places where expressions are used in the syntax instead of conditions is in expression statements and on the right-hand side of assignment statements; this catches some nasty bugs like accidentally writing \verb@x == 1@ instead of \verb@x = 1@. \indexii{assignment}{statement} The comma plays several roles in Python's syntax. It is usually an operator with a lower precedence than all others, but occasionally serves other purposes as well; e.g. it separates function arguments, is used in list and dictionary constructors, and has special semantics in \verb@print@ statements. \index{comma} When (one alternative of) a syntax rule has the form \begin{verbatim} name: othername \end{verbatim} and no semantics are given, the semantics of this form of \verb@name@ are the same as for \verb@othername@. \index{syntax} \section{Arithmetic conversions} \indexii{arithmetic}{conversion} When a description of an arithmetic operator below uses the phrase ``the numeric arguments are converted to a common type'', this both means that if either argument is not a number, a \verb@TypeError@ exception is raised, and that otherwise the following conversions are applied: \exindex{TypeError} \indexii{floating point}{number} \indexii{long}{integer} \indexii{plain}{integer} \begin{itemize} \item first, if either argument is a floating point number, the other is converted to floating point; \item else, if either argument is a long integer, the other is converted to long integer; \item otherwise, both must be plain integers and no conversion is necessary. \end{itemize} \section{Atoms} \index{atom} Atoms are the most basic elements of expressions. Forms enclosed in reverse quotes or in parentheses, brackets or braces are also categorized syntactically as atoms. The syntax for atoms is: \begin{verbatim} atom: identifier | literal | enclosure enclosure: parenth_form|list_display|dict_display|string_conversion \end{verbatim} \subsection{Identifiers (Names)} \index{name} \index{identifier} An identifier occurring as an atom is a reference to a local, global or built-in name binding. If a name is assigned to anywhere in a code block (even in unreachable code), and is not mentioned in a \verb@global@ statement in that code block, then it refers to a local name throughout that code block. When it is not assigned to anywhere in the block, or when it is assigned to but also explicitly listed in a \verb@global@ statement, it refers to a global name if one exists, else to a built-in name (and this binding may dynamically change). \indexii{name}{binding} \index{code block} \stindex{global} \indexii{built-in}{name} \indexii{global}{name} When the name is bound to an object, evaluation of the atom yields that object. When a name is not bound, an attempt to evaluate it raises a \verb@NameError@ exception. \exindex{NameError} \subsection{Literals} \index{literal} Python knows string and numeric literals: \begin{verbatim} literal: stringliteral | integer | longinteger | floatnumber \end{verbatim} Evaluation of a literal yields an object of the given type (string, integer, long integer, floating point number) with the given value. The value may be approximated in the case of floating point literals. See section \ref{literals} for details. All literals correspond to immutable data types, and hence the object's identity is less important than its value. Multiple evaluations of literals with the same value (either the same occurrence in the program text or a different occurrence) may obtain the same object or a different object with the same value. \indexiii{immutable}{data}{type} (In the original implementation, all literals in the same code block with the same type and value yield the same object.) \subsection{Parenthesized forms} \index{parenthesized form} A parenthesized form is an optional condition list enclosed in parentheses: \begin{verbatim} parenth_form: "(" [condition_list] ")" \end{verbatim} A parenthesized condition list yields whatever that condition list yields. An empty pair of parentheses yields an empty tuple object. Since tuples are immutable, the rules for literals apply here. \indexii{empty}{tuple} (Note that tuples are not formed by the parentheses, but rather by use of the comma operator. The exception is the empty tuple, for which parentheses {\em are} required --- allowing unparenthesized ``nothing'' in expressions would cause ambiguities and allow common typos to pass uncaught.) \index{comma} \indexii{tuple}{display} \subsection{List displays} \indexii{list}{display} A list display is a possibly empty series of conditions enclosed in square brackets: \begin{verbatim} list_display: "[" [condition_list] "]" \end{verbatim} A list display yields a new list object. \obindex{list} If it has no condition list, the list object has no items. Otherwise, the elements of the condition list are evaluated from left to right and inserted in the list object in that order. \indexii{empty}{list} \subsection{Dictionary displays} \label{dict} \indexii{dictionary}{display} A dictionary display is a possibly empty series of key/datum pairs enclosed in curly braces: \index{key} \index{datum} \index{key/datum pair} \begin{verbatim} dict_display: "{" [key_datum_list] "}" key_datum_list: key_datum ("," key_datum)* [","] key_datum: condition ":" condition \end{verbatim} A dictionary display yields a new dictionary object. \obindex{dictionary} The key/datum pairs are evaluated from left to right to define the entries of the dictionary: each key object is used as a key into the dictionary to store the corresponding datum. Restrictions on the types of the key values are listed earlier in section \ref{types}. Clashes between duplicate keys are not detected; the last datum (textually rightmost in the display) stored for a given key value prevails. \exindex{TypeError} \subsection{String conversions} \indexii{string}{conversion} \indexii{reverse}{quotes} \indexii{backward}{quotes} \index{back-quotes} A string conversion is a condition list enclosed in reverse (or backward) quotes: \begin{verbatim} string_conversion: "`" condition_list "`" \end{verbatim} A string conversion evaluates the contained condition list and converts the resulting object into a string according to rules specific to its type. If the object is a string, a number, \verb@None@, or a tuple, list or dictionary containing only objects whose type is one of these, the resulting string is a valid Python expression which can be passed to the built-in function \verb@eval()@ to yield an expression with the same value (or an approximation, if floating point numbers are involved). (In particular, converting a string adds quotes around it and converts ``funny'' characters to escape sequences that are safe to print.) It is illegal to attempt to convert recursive objects (e.g. lists or dictionaries that contain a reference to themselves, directly or indirectly.) \obindex{recursive} The built-in function \verb@repr()@ performs exactly the same conversion in its argument as enclosing it it reverse quotes does. The built-in function \verb@str()@ performs a similar but more user-friendly conversion. \bifuncindex{repr} \bifuncindex{str} \section{Primaries} \label{primaries} \index{primary} Primaries represent the most tightly bound operations of the language. Their syntax is: \begin{verbatim} primary: atom | attributeref | subscription | slicing | call \end{verbatim} \subsection{Attribute references} \indexii{attribute}{reference} An attribute reference is a primary followed by a period and a name: \begin{verbatim} attributeref: primary "." identifier \end{verbatim} The primary must evaluate to an object of a type that supports attribute references, e.g. a module or a list. This object is then asked to produce the attribute whose name is the identifier. If this attribute is not available, the exception \verb@AttributeError@ is raised. Otherwise, the type and value of the object produced is determined by the object. Multiple evaluations of the same attribute reference may yield different objects. \obindex{module} \obindex{list} \subsection{Subscriptions} \index{subscription} A subscription selects an item of a sequence (string, tuple or list) or mapping (dictionary) object: \obindex{sequence} \obindex{mapping} \obindex{string} \obindex{tuple} \obindex{list} \obindex{dictionary} \indexii{sequence}{item} \begin{verbatim} subscription: primary "[" condition "]" \end{verbatim} The primary must evaluate to an object of a sequence or mapping type. If it is a mapping, the condition must evaluate to an object whose value is one of the keys of the mapping, and the subscription selects the value in the mapping that corresponds to that key. If it is a sequence, the condition must evaluate to a plain integer. If this value is negative, the length of the sequence is added to it (so that, e.g. \verb@x[-1]@ selects the last item of \verb@x@.) The resulting value must be a nonnegative integer smaller than the number of items in the sequence, and the subscription selects the item whose index is that value (counting from zero). A string's items are characters. A character is not a separate data type but a string of exactly one character. \index{character} \indexii{string}{item} \subsection{Slicings} \index{slicing} \index{slice} A slicing (or slice) selects a range of items in a sequence (string, tuple or list) object: \obindex{sequence} \obindex{string} \obindex{tuple} \obindex{list} \begin{verbatim} slicing: primary "[" [condition] ":" [condition] "]" \end{verbatim} The primary must evaluate to a sequence object. The lower and upper bound expressions, if present, must evaluate to plain integers; defaults are zero and the sequence's length, respectively. If either bound is negative, the sequence's length is added to it. The slicing now selects all items with index \var{k} such that \code{\var{i} <= \var{k} < \var{j}} where \var{i} and \var{j} are the specified lower and upper bounds. This may be an empty sequence. It is not an error if \var{i} or \var{j} lie outside the range of valid indexes (such items don't exist so they aren't selected). \subsection{Calls} \label{calls} \index{call} A call calls a callable object (e.g. a function) with a possibly empty series of arguments:\footnote{The new syntax for keyword arguments is not yet documented in this manual. See chapter 12 of the Tutorial.} \obindex{callable} \begin{verbatim} call: primary "(" [condition_list] ")" \end{verbatim} The primary must evaluate to a callable object (user-defined functions, built-in functions, methods of built-in objects, class objects, and methods of class instances are callable). If it is a class, the argument list must be empty; otherwise, the arguments are evaluated. A call always returns some value, possibly \verb@None@, unless it raises an exception. How this value is computed depends on the type of the callable object. If it is: \begin{description} \item[a user-defined function:] the code block for the function is executed, passing it the argument list. The first thing the code block will do is bind the formal parameters to the arguments; this is described in section \ref{function}. When the code block executes a \verb@return@ statement, this specifies the return value of the function call. \indexii{function}{call} \indexiii{user-defined}{function}{call} \obindex{user-defined function} \obindex{function} \item[a built-in function or method:] the result is up to the interpreter; see the library reference manual for the descriptions of built-in functions and methods. \indexii{function}{call} \indexii{built-in function}{call} \indexii{method}{call} \indexii{built-in method}{call} \obindex{built-in method} \obindex{built-in function} \obindex{method} \obindex{function} \item[a class object:] a new instance of that class is returned. \obindex{class} \indexii{class object}{call} \item[a class instance method:] the corresponding user-defined function is called, with an argument list that is one longer than the argument list of the call: the instance becomes the first argument. \obindex{class instance} \obindex{instance} \indexii{instance}{call} \indexii{class instance}{call} \end{description} \section{Unary arithmetic operations} \indexiii{unary}{arithmetic}{operation} \indexiii{unary}{bit-wise}{operation} All unary arithmetic (and bit-wise) operations have the same priority: \begin{verbatim} u_expr: primary | "-" u_expr | "+" u_expr | "~" u_expr \end{verbatim} The unary \verb@"-"@ (minus) operator yields the negation of its numeric argument. \index{negation} \index{minus} The unary \verb@"+"@ (plus) operator yields its numeric argument unchanged. \index{plus} The unary \verb@"~"@ (invert) operator yields the bit-wise inversion of its plain or long integer argument. The bit-wise inversion of \verb@x@ is defined as \verb@-(x+1)@. \index{inversion} In all three cases, if the argument does not have the proper type, a \verb@TypeError@ exception is raised. \exindex{TypeError} \section{Binary arithmetic operations} \indexiii{binary}{arithmetic}{operation} The binary arithmetic operations have the conventional priority levels. Note that some of these operations also apply to certain non-numeric types. There is no ``power'' operator, so there are only two levels, one for multiplicative operators and one for additive operators: \begin{verbatim} m_expr: u_expr | m_expr "*" u_expr | m_expr "/" u_expr | m_expr "%" u_expr a_expr: m_expr | aexpr "+" m_expr | aexpr "-" m_expr \end{verbatim} The \verb@"*"@ (multiplication) operator yields the product of its arguments. The arguments must either both be numbers, or one argument must be a plain integer and the other must be a sequence. In the former case, the numbers are converted to a common type and then multiplied together. In the latter case, sequence repetition is performed; a negative repetition factor yields an empty sequence. \index{multiplication} The \verb@"/"@ (division) operator yields the quotient of its arguments. The numeric arguments are first converted to a common type. Plain or long integer division yields an integer of the same type; the result is that of mathematical division with the `floor' function applied to the result. Division by zero raises the \verb@ZeroDivisionError@ exception. \exindex{ZeroDivisionError} \index{division} The \verb@"%"@ (modulo) operator yields the remainder from the division of the first argument by the second. The numeric arguments are first converted to a common type. A zero right argument raises the \verb@ZeroDivisionError@ exception. The arguments may be floating point numbers, e.g. \verb@3.14 % 0.7@ equals \verb@0.34@. The modulo operator always yields a result with the same sign as its second operand (or zero); the absolute value of the result is strictly smaller than the second operand. \index{modulo} The integer division and modulo operators are connected by the following identity: \verb@x == (x/y)*y + (x%y)@. Integer division and modulo are also connected with the built-in function \verb@divmod()@: \verb@divmod(x, y) == (x/y, x%y)@. These identities don't hold for floating point numbers; there a similar identity holds where \verb@x/y@ is replaced by \verb@floor(x/y)@). The \verb@"+"@ (addition) operator yields the sum of its arguments. The arguments must either both be numbers, or both sequences of the same type. In the former case, the numbers are converted to a common type and then added together. In the latter case, the sequences are concatenated. \index{addition} The \verb@"-"@ (subtraction) operator yields the difference of its arguments. The numeric arguments are first converted to a common type. \index{subtraction} \section{Shifting operations} \indexii{shifting}{operation} The shifting operations have lower priority than the arithmetic operations: \begin{verbatim} shift_expr: a_expr | shift_expr ( "<<" | ">>" ) a_expr \end{verbatim} These operators accept plain or long integers as arguments. The arguments are converted to a common type. They shift the first argument to the left or right by the number of bits given by the second argument. A right shift by \var{n} bits is defined as division by \code{pow(2,\var{n})}. A left shift by \var{n} bits is defined as multiplication with \code{pow(2,\var{n})}; for plain integers there is no overflow check so this drops bits and flips the sign if the result is not less than \code{pow(2,31)} in absolute value. Negative shift counts raise a \verb@ValueError@ exception. \exindex{ValueError} \section{Binary bit-wise operations} \indexiii{binary}{bit-wise}{operation} Each of the three bitwise operations has a different priority level: \begin{verbatim} and_expr: shift_expr | and_expr "&" shift_expr xor_expr: and_expr | xor_expr "^" and_expr or_expr: xor_expr | or_expr "|" xor_expr \end{verbatim} The \verb@"&"@ operator yields the bitwise AND of its arguments, which must be plain or long integers. The arguments are converted to a common type. \indexii{bit-wise}{and} The \verb@"^"@ operator yields the bitwise XOR (exclusive OR) of its arguments, which must be plain or long integers. The arguments are converted to a common type. \indexii{bit-wise}{xor} \indexii{exclusive}{or} The \verb@"|"@ operator yields the bitwise (inclusive) OR of its arguments, which must be plain or long integers. The arguments are converted to a common type. \indexii{bit-wise}{or} \indexii{inclusive}{or} \section{Comparisons} \index{comparison} Contrary to C, all comparison operations in Python have the same priority, which is lower than that of any arithmetic, shifting or bitwise operation. Also contrary to C, expressions like \verb@a < b < c@ have the interpretation that is conventional in mathematics: \index{C} \begin{verbatim} comparison: or_expr (comp_operator or_expr)* comp_operator: "<"|">"|"=="|">="|"<="|"<>"|"!="|"is" ["not"]|["not"] "in" \end{verbatim} Comparisons yield integer values: 1 for true, 0 for false. Comparisons can be chained arbitrarily, e.g. \code{x < y <= z} is equivalent to \code{x < y and y <= z}, except that \code{y} is evaluated only once (but in both cases \code{z} is not evaluated at all when \code{x < y} is found to be false). \indexii{chaining}{comparisons} Formally, if \var{a}, \var{b}, \var{c}, \ldots, \var{y}, \var{z} are expressions and \var{opa}, \var{opb}, \ldots, \var{opy} are comparison operators, then \var{a opa b opb c} \ldots \var{y opy z} is equivalent to \var{a opa b} \code{and} \var{b opb c} \code{and} \ldots \code{and} \var{y opy z}, except that each expression is evaluated at most once. Note that \var{a opa b opb c} doesn't imply any kind of comparison between \var{a} and \var{c}, so that e.g.\ \code{x < y > z} is perfectly legal (though perhaps not pretty). The forms \verb@<>@ and \verb@!=@ are equivalent; for consistency with C, \verb@!=@ is preferred; where \verb@!=@ is mentioned below \verb@<>@ is also implied. The operators {\tt "<", ">", "==", ">=", "<="}, and {\tt "!="} compare the values of two objects. The objects needn't have the same type. If both are numbers, they are coverted to a common type. Otherwise, objects of different types {\em always} compare unequal, and are ordered consistently but arbitrarily. (This unusual definition of comparison is done to simplify the definition of operations like sorting and the \verb@in@ and \verb@not@ \verb@in@ operators.) Comparison of objects of the same type depends on the type: \begin{itemize} \item Numbers are compared arithmetically. \item Strings are compared lexicographically using the numeric equivalents (the result of the built-in function \verb@ord@) of their characters. \item Tuples and lists are compared lexicographically using comparison of corresponding items. \item Mappings (dictionaries) are compared through lexicographic comparison of their sorted (key, value) lists.% \footnote{This is expensive since it requires sorting the keys first, but about the only sensible definition. An earlier version of Python compared dictionaries by identity only, but this caused surprises because people expected to be able to test a dictionary for emptiness by comparing it to {\tt \{\}}.} \item Most other types compare unequal unless they are the same object; the choice whether one object is considered smaller or larger than another one is made arbitrarily but consistently within one execution of a program. \end{itemize} The operators \verb@in@ and \verb@not in@ test for sequence membership: if \var{y} is a sequence, \code{\var{x} in \var{y}} is true if and only if there exists an index \var{i} such that \code{\var{x} = \var{y}[\var{i}]}. \code{\var{x} not in \var{y}} yields the inverse truth value. The exception \verb@TypeError@ is raised when \var{y} is not a sequence, or when \var{y} is a string and \var{x} is not a string of length one.% \footnote{The latter restriction is sometimes a nuisance.} \opindex{in} \opindex{not in} \indexii{membership}{test} \obindex{sequence} The operators \verb@is@ and \verb@is not@ test for object identity: \var{x} \code{is} \var{y} is true if and only if \var{x} and \var{y} are the same object. \var{x} \code{is not} \var{y} yields the inverse truth value. \opindex{is} \opindex{is not} \indexii{identity}{test} \section{Boolean operations} \label{Booleans} \indexii{Boolean}{operation} Boolean operations have the lowest priority of all Python operations: \begin{verbatim} condition: or_test | lambda_form or_test: and_test | or_test "or" and_test and_test: not_test | and_test "and" not_test not_test: comparison | "not" not_test lambda_form: "lambda" [parameter_list]: condition \end{verbatim} In the context of Boolean operations, and also when conditions are used by control flow statements, the following values are interpreted as false: \verb@None@, numeric zero of all types, empty sequences (strings, tuples and lists), and empty mappings (dictionaries). All other values are interpreted as true. The operator \verb@not@ yields 1 if its argument is false, 0 otherwise. \opindex{not} The condition \var{x} \verb@and@ \var{y} first evaluates \var{x}; if \var{x} is false, its value is returned; otherwise, \var{y} is evaluated and the resulting value is returned. \opindex{and} The condition \var{x} \verb@or@ \var{y} first evaluates \var{x}; if \var{x} is true, its value is returned; otherwise, \var{y} is evaluated and the resulting value is returned. \opindex{or} (Note that \verb@and@ and \verb@or@ do not restrict the value and type they return to 0 and 1, but rather return the last evaluated argument. This is sometimes useful, e.g. if \verb@s@ is a string that should be replaced by a default value if it is empty, the expression \verb@s or 'foo'@ yields the desired value. Because \verb@not@ has to invent a value anyway, it does not bother to return a value of the same type as its argument, so e.g. \verb@not 'foo'@ yields \verb@0@, not \verb@''@.) Lambda forms (lambda expressions) have the same syntactic position as conditions. They are a shorthand to create anonymous functions; the expression {\em {\tt lambda} arguments{\tt :} condition} yields a function object that behaves virtually identical to one defined with {\em {\tt def} name {\tt (}arguments{\tt ): return} condition}. See section \ref{function} for the syntax of parameter lists. Note that functions created with lambda forms cannot contain statements. \label{lambda} \indexii{lambda}{expression} \indexii{lambda}{form} \indexii{anonmymous}{function} \section{Expression lists and condition lists} \indexii{expression}{list} \indexii{condition}{list} \begin{verbatim} expression_list: or_expr ("," or_expr)* [","] condintion_list: condition ("," condition)* [","] \end{verbatim} The only difference between expression lists and condition lists is the lowest priority of operators that can be used in them without being enclosed in parentheses; condition lists allow all operators, while expression lists don't allow comparisons and Boolean operators (they do allow bitwise and shift operators though). Expression lists are used in expression statements and assignments; condition lists are used everywhere else where a list of comma-separated values is required. An expression (condition) list containing at least one comma yields a tuple. The length of the tuple is the number of expressions (conditions) in the list. The expressions (conditions) are evaluated from left to right. (Condition lists are used syntactically is a few places where no tuple is constructed but a list of values is needed nevertheless.) \obindex{tuple} The trailing comma is required only to create a single tuple (a.k.a. a {\em singleton}); it is optional in all other cases. A single expression (condition) without a trailing comma doesn't create a tuple, but rather yields the value of that expression (condition). \indexii{trailing}{comma} (To create an empty tuple, use an empty pair of parentheses: \verb@()@.) \section{Summary} The following table summarizes the operator precedences in Python, from lowest precedence (least binding) to highest precedence (most binding). Operators in the same box have the same precedence. Unless the syntax is explicitly given, operators are binary. Operators in the same box group left to right (except for comparisons, which chain from left to right --- see above). \begin{center} \begin{tabular}{|c|c|} \hline \code{or} & Boolean OR \\ \hline \code{and} & Boolean AND \\ \hline \code{not} \var{x} & Boolean NOT \\ \hline \code{in}, \code{not} \code{in} & Membership tests \\ \code{is}, \code{is} \code{not} & Identity tests \\ \code{<}, \code{<=}, \code{>}, \code{>=}, \code{<>}, \code{!=}, \code{=} & Comparisons \\ \hline \code{|} & Bitwise OR \\ \hline \code{\^} & Bitwise XOR \\ \hline \code{\&} & Bitwise AND \\ \hline \code{<<}, \code{>>} & Shifts \\ \hline \code{+}, \code{-} & Addition and subtraction \\ \hline \code{*}, \code{/}, \code{\%} & Multiplication, division, remainder \\ \hline \code{+\var{x}}, \code{-\var{x}} & Positive, negative \\ \code{\~\var{x}} & Bitwise not \\ \hline \code{\var{x}.\var{attribute}} & Attribute reference \\ \code{\var{x}[\var{index}]} & Subscription \\ \code{\var{x}[\var{index}:\var{index}]} & Slicing \\ \code{\var{f}(\var{arguments}...)} & Function call \\ \hline \code{(\var{expressions}\ldots)} & Binding or tuple display \\ \code{[\var{expressions}\ldots]} & List display \\ \code{\{\var{key}:\var{datum}\ldots\}} & Dictionary display \\ \code{`\var{expression}\ldots`} & String conversion \\ \hline \end{tabular} \end{center}


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